To find the midpoint of a line segment whose endpoints are [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula. The midpoint formula is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Let's apply this formula step by step for the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/tex]:
1. Add the [tex]\(x\)[/tex]-coordinates of the endpoints:
[tex]\[
x_1 + x_2 = 3.5 + 1.5 = 5.0
\][/tex]
2. Divide the sum by 2 to find the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{5.0}{2} = 2.5
\][/tex]
3. Add the [tex]\(y\)[/tex]-coordinates of the endpoints:
[tex]\[
y_1 + y_2 = 2.2 + (-4.8) = 2.2 - 4.8 = -2.6
\][/tex]
4. Divide the sum by 2 to find the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-2.6}{2} = -1.3
\][/tex]
Thus, the coordinates of the midpoint are [tex]\((2.5, -1.3)\)[/tex].
Therefore, the correct answer is:
A. [tex]\((2.5, -1.3)\)[/tex]
